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Math Help - Question regarding Composite fxns with fractions

  1. #1
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    Question Question regarding Composite fxns with fractions

    These are the two fxns

    f(x) = (x+1)/(x-1)

    g(x) = 1/x

    I have to find f o g and f o f.

    I tried to work it out but in f o g, it's too confusing what to do with the fraction in a fraction and in f o f it's in the num and denom.

    I know the answers but not how to solve...

    f o g = (1 + x)/ (1 - x)

    f o f = X

    Please help to find how to solve this! Thanks.
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  2. #2
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    Quote Originally Posted by D-Rose View Post
    These are the two fxns

    f(x) = (x+1)/(x-1)

    g(x) = 1/x

    I have to find f o g and f o f.

    I tried to work it out but in f o g, it's too confusing what to do with the fraction in a fraction and in f o f it's in the num and denom.

    I know the answers but not how to solve...

    f o g = (1 + x)/ (1 - x)

    f o f = X

    Please help to find how to solve this! Thanks.
    \displaystyle\ g(x)=\frac{1}{x}

    \displaystyle\ f[g(x)]=\frac{g(x)+1}{g(x)-1}=\frac{\frac{1}{x}+1}{\frac{1}{x}-1}=\frac{\left(\frac{x+1}{x}\right)}{\left(\frac{1-x}{x}\right)}=\frac{1+x}{1-x}

    Try f[f(x)]
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  3. #3
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    I don't understand how you went from Step 2 to 3...did something with the reciprocal of one of the fractions?
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  4. #4
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    Quote Originally Posted by D-Rose View Post
    I don't understand how you went from Step 2 to 3...did something with the reciprocal of one of the fractions?
    Hi, you probably need some practice combining fractions.
    Is the following ok?

    \displaystyle\frac{\frac{1}{x}+1}{\frac{1}{x}-1}=\frac{\frac{1}{x}+\frac{x}{x}}{\frac{1}{x}-\frac{x}{x}}=\frac{\left(\frac{1}{x}\right)}{\left  (\frac{1}{x}\right)}\ \frac{1+x}{1-x}<br />
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  5. #5
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    Wow haha, I knew that but didn't think. Thanks!
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